“Enter” the journey of proving Ngo Bao Chau’s basic lemma

Recently, the press has talked a lot about Professor Ngo Bao Chau. What did your parents do before? Where did you study and what awards did you receive? In which city did you receive the Fields Award and who awarded the medal? Even The press said his work was 169 pages long (169 pages!) and the name of the publisher publishing the magazine that published the work

However, the press There is little mention of the work he did – the work that made him a worthy recipient of the Fields Award. “In general, he is good at math” is the rough concept of most authors of related articles . That concept is often expressed in very grand language but is still a rudimentary concept.

Authors often stop at the sentence “Ngo Bao Chau has proven that” Basic Lemma” (occasionally add a little French to it: “Le lemme fondamental pour les algèbres de Lie”). But what is “Basic Lemma”and whyc< /span>prove it?

I’m not good at math, but I think scientific issues can be expressed in interesting and easy-to-understand language if the author takes a little time study. I did research and found the story so interesting that it would be such a waste not to tell you…

The story begins like this. A long time ago, mathematicians announced two important theories: number theory and group theory. I will let “Wiki” explain the nature of those two theories – what should be remembered is that (a) those two theories are very important in the world. mathematical world and (b) those two theories from afar look separate from each other like two branches of a tree trunk.

About 30 years ago a Canadian mathematician named Robert Langlands announced that he thought the two theories were variously related. Robert’s views (and the way he expressed them) shocked many mathematicians! Robert shocked himself too – he stated that it would take several generations to prove the related diversity that he thought existed.

“But the first step will be relatively easy to do,” Mr. Robert confidently told his colleagues.

That “first step” Robert named “fundamental lemma” and that is it. is “Basic Lemma” that you have heard a lot about recently.

Mr. Robert seemed to be standing on a small island looking towards East is a big ship. Looking to the West is also a big ship. (Two unmanned ships floating on the sea.) Robert couldn’t look closely but still thought the two ships had many things in common. Yes When producing the same type of steel, sometimes the propeller of the “Eastern ship” points to the right, and the rudder of the “Western ship” will automatically point to the left /p>

Needless to say, those two ships are number theory and group theory.

For Robert the proof of the “basic lemma” can be compared to the throwing of two hooked ropes to two ships. When that was done, the healthy mathematicians could stand on the island with Robert and use the rope to pull the two ships together. (Only then did a closer look to find the connection.) Pulling the two ships together and comparing was something Robert thought would take several generations. But throwing those two hooked ropes, Mr. Robert thought, would be quick.

But Mr. Robert was wrong. Throwing the rope is very difficult. Robert and some students tried throwing several times but failed every time. They only know how to throw close (not accurately) and use thin strings.

Robert’s island became a famous island. For 30 years, many mathematicians came to “try it.” Everyone wiped their sweat and exclaimed “so difficult!” Many mathematicians on the mainland prepared tools to test and compare the two ships when they were towed to the island (towed close together!). They produce machines to test paint types that program software to analyze two propellers. Some people even practice sailing and standing on the deck to avoid seasickness. All that work and practice will be meaningless if there is no one to throw the rope accurately.

And then Mr. Ngo Bao Chau appeared. Hearing about Robert’s island, he swam over and asked to try throwing. “Okay!” encouraged by the world’s best mathematicians. “You can try it as many times as you want and then sit with us and drink iced tea!”

Anh Chau tried one very strong throw using the heaviest rope. The other mathematicians stood up and were surprised, many cups of iced tea fell to the ground. Mr. Chau’s throwing style is very strange; He used special techniques that no one had ever seen before. “Throw it really, brother!” Mathematicians continued to encourage. “Who knows, maybe you’ll be the first mathematician to catch a train with both hands!”

Ngo Bao Chau actually threw it. And exactly. The two hooks stuck to the two ships and everyone immediately applauded loudly. Then Chau told the mathematicians standing on Robert Island to help him hold the rope (and started pulling the two ships close together) so he could go to India. received the Fields Award.

The story ends here.

Proving the “Basic Lemma” is one of the greatest successes of modern mathematics, voted by Time magazine as one of the 10 outstanding scientific inventions of the year 2009. Because Ngo Bao Chau has completed this work, in the coming years, world scientists can confidently research the relationship between number theory and group theory. It was truly a wonderful achievement – ​​all of Vietnam should be proud of the rope thrower named Ngo Bao Chau.

Joe